Details

Time bar (total: 7.2s)

sample30.0ms

Algorithm
intervals
Results
10.0ms279×body80valid
4.0ms106×body80nan

simplify44.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12214
24514
36914
49314
510614
done10614

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
3.0b
(* (* x y) z)
8.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms
(sqrt (- (* z z) (* t a)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
86.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify605.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (130.0ms)

IterNodesCost
01461331
13721224
218061062
done50001062

prune298.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
1.6b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num *-commutative
Counts
4 → 122
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
22.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ z (sqrt (- (* z z) (* t a))))
38.0ms
(- (* z z) (* t a))
88.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify750.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (156.0ms)

IterNodesCost
01782135
14581955
220351740
done50011740

prune342.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.8b
(- (* z z) (* t a))
1.8b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
8.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
5.0ms
(sqrt (- (* z z) (* t a)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (sqrt (- (* z z) (* t a))) z)
33.0ms
(- (* z z) (* t a))
85.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify774.0ms

Counts
154 → 154
Iterations

Useful iterations: 2 (173.0ms)

IterNodesCost
02222758
15522525
223702314
done50002314

prune420.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.8b
(- (* z z) (* t a))
1.8b
(/ (* x y) (pow (/ (sqrt (- (* z z) (* t a))) z) 1))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
49×add-sqr-sqrt
48×add-cube-cbrt *-un-lft-identity
44×unpow-prod-down
33×sqrt-prod
29×associate-/r*
26×add-exp-log
11×div-exp add-cbrt-cube
7×associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div pow-exp prod-exp log1p-expm1-u div-inv
3×cbrt-undiv flip3-- flip--
2×pow-to-exp frac-2neg clear-num associate-/l/ sqr-pow
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff cbrt-unprod
Counts
4 → 151
Calls
4 calls:
7.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
19.0ms
(/ (* x y) (pow (/ (sqrt (- (* z z) (* t a))) z) 1))
5.0ms
(sqrt (- (* z z) (* t a)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (sqrt (- (* z z) (* t a))) z)
34.0ms
(- (* z z) (* t a))
287.0ms
(/ (* x y) (pow (/ (sqrt (- (* z z) (* t a))) z) 1))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify875.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (207.0ms)

IterNodesCost
02743110
16162652
225952412
done50002412

prune426.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

regimes389.0ms

Accuracy

84.7% (3.1b remaining)

Error of 6.3b against oracle of 3.2b and baseline of 23.5b

bsearch77.0ms

Steps
ItersRangePoint
10
8.756260439201689e+104
1.7016018298191544e+118
1.0315608467704857e+107
5
-3.1723327532004586e+140
-8.095784603387317e+139
-1.5734058117429052e+140

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02131
12929
23129
done3129

end0.0ms

sample782.0ms

Algorithm
intervals
Results
328.0ms8836×body80valid
105.0ms2919×body80nan